Supplementary Materials

Measurements as a function of temperature up to 1.4 K are reported in Fig. \ref{figure:appendix}a for the sFS side of the SIsFS A device. From each IV curve of the SIsFS JJ A in the inset of Fig. \ref{figure:appendix}b, the gap voltage \( 2 \Delta / e\) (Fig. \ref{figure:appendix}b) and the \(I_{sw}R_{N}\) product (Fig. \ref{figure:appendix}c) have been extracted. The experimental temperature dependence \( 2 \Delta / e\) follows the Bardeen-Cooper-Schrieffer (BCS) approximation in the weak-coupling limit: \(\frac{2 \Delta(T)} {e} = \frac{2 \Delta_{0}}{e} \tanh \left ( 1.74 \sqrt{1 - \frac{T}{T_{c}}} \right )\) \cite{Barone1982}. The fit reported in Fig. \ref{figure:appendix}b provides the zero temperature $ V_{gap} = 440 \pm 20 \mu \textrm{eV}$ and $T_c = 1.3 \pm 0.1$. The \(I_{sw}R_{N}(T)\) curves follow the Ambegaokar-Baratoff (AB) relation \cite{AB_theory}: \(I_{sw}R_{N}(T) = A \frac{\pi}{2e} \Delta(T)\tanh \left ( \frac{\Delta(T)}{2k_{B}T} \right )\). In this case, we have introduced a coefficient \(A\) to taken into account the suppression of the critical current with respect to the ideal case, which is equal to $0.18 \pm 0.02$.